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Validity and Truth

Validity and Truth. Unit – 1 Chapter – 5 Tutor : Dhundi Raj Giri. Validity and Truth: Meaning . 1. Validity: A piece of information that can be trusted or believed. Or Any argument or comment or idea that is based on the sensible reasoning or that is real in the world outside.

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Validity and Truth

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  1. Validity and Truth Unit – 1 Chapter – 5 Tutor : Dhundi Raj Giri

  2. Validity and Truth: Meaning 1. Validity: • A piece of information that can be trusted or believed. Or • Any argument or comment or idea that is based on the sensible reasoning or that is real in the world outside. • Truth: • Truth is something that is based on the facts or that can be believed to be true. Or • Truth is the quality of being true or real.

  3. Validity in Logic: • Validity refers to the relation between its propositions – between the set of propositions that serve as premises and the one proposition that serves as conclusion of that argument. • If the conclusion follows with logical necessity orsensible reasoning from its premises then it is a valid argument. • Therefore validity can never apply to any single proposition by itself. • Because the needed relation can not be found within any one single proposition.

  4. Truth in Logic: • Truth and falsity are the attributes of individual propositions. • A single statement that serve as a premise in an argument may or may not be true. • The statement that serve as its conclusion may be false. • Truth is the quality of a proposition that asserts what really is the case.

  5. Contd… • E.g. “Amazon river is the biggest river in the world.” Or • Nile is the longest river in the world. • It is true because it really is the case. • But if I say “ Nile is the Biggest river in the world.” it is not the case. It is false. • Therefore, Truth and Falsity are the attributes of individual propositions whereas Validity and Invalidity are the attributes of arguments.

  6. Contd… • The concept of validity can not be applied to single propositions likewise, the concept of truth can not be applied to arguments. • Of the several propositions in an argument, some (or all) may be true and some (or all) may be false. • But the validity or invalidity of an argument depends on the sensible reasoning of the conclusion followed by premises.

  7. Contd… • An argument may be valid even when its one or more of its premises are false. 1. Some valid arguments contain only true propositions – true premises and a true conclusion. E.g. All mammals have lungs. (premises) All whales are mammals. (premise) Therefore all whales have lungs. (conclusion) Structure: Two true premises + one true conclusion Such arguments are called sound arguments.

  8. Contd… 2. Some valid arguments contain only false propositions – a false conclusion. E.g. All four legged creatures have wings. (premise) All spiders have four legs. (premise) Therefore all spiders have wings. (conclusion) Structure: two false premises + false conclusion

  9. Contd… 3. Some invalid arguments contain only true propositions – all the premises are true and their conclusion is also true. • If I owned all the money in the Nepal Rastra Bank, then I would be wealthy. • I do not own all the money in the Nepal Rastra Bank. • Therefore I am not wealthy. 4. Some invalid arguments contain only true premises and have a false conclusion.

  10. Contd… • If Mr. Jha owned all the money in the Nepal Rastra Bank, then Mr. |Jha would be wealthy. • Mr. Jha does not own all the gold in the Nepal Rastra Bank. • Therefore, Mr. Jha is not wealthy. 5. Some valid arguments have false premises and a true conclusion. E.g. • All fishes are mammals. • All whales are fishes. • Therefore, all whales are mammals

  11. Contd… 6. Some invalid arguments also have false premises and a true conclusion. E.g. • All mammals have wings. • All whales have wings. • Therefore all whales are mammals. 7. Some invalid arguments contain all false propositions – false premises and false conclusion. • All mammals have wings. • All whales have wings. • Therefore all mammals are whales.

  12. Invalid Arguments:

  13. Valid Arguments:

  14. Exercise: • Construct a series of deductive arguments, on any subject of your choice each with only two premises, having the following characteristics: • A valid argument with one true premise, one false premise, and a false conclusion. • A valid argument with one true premise, one false premise, and a true conclusion. • An invalid argument with two premises and a false conclusion.

  15. Exercise: 4. An invalid argument with two true premises and a true conclusion. 5. A valid argument with two false premises and a true conclusion. 6. An invalid argument with two false premises and a true conclusion. 7. An invalid argument with one true premise, one false premise, and a true conclusion. 8. A valid argument with two true premises and a true conclusion.

  16. Thank You

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